Civitello et al. 2015

1. Linking existing theory and data

• Competence, extirpation risk, and life history

1. Linking existing theory and data

• Competence, extirpation risk, and life history
• Modes of transmission

Frequency vs. density-dependent

Frequency-dependent (FD) vs. density-dependent (DD) vs.

Constant risk:

\(\dfrac{dI}{dt} = \beta S\)

Power law:

\(\dfrac{dI}{dt} = \beta S I^q\)

\(\dfrac{dI}{dt} = \beta S^p I^q\)

Negative binomial:

\(\dfrac{dI}{dt} = (kS) log(1 + \frac{\beta I}{k})\)

Theory

Little known beyond FD and DD transmission

Theory

Little known beyond FD and DD transmission

Data

Suggests support beyond FD and DD

(i.e. 'non-linear' transmission functions)

(Orlofske et al. in prep)

1. Linking existing theory and data

• Competence, extirpation risk, and life history
• Modes of transmission
• Competition (among hosts and parasites)

Effect of richness depends on interaction between competition and transmission

Strauss et al. 2015

watch for O'Reagan et al. in press AmNat

Multi-host, multi-parasite systems:

• interaction between host and parasite diversity?
• role of competition?
• evolution and diversity?
• mathematical tractability?

1. Linking existing theory and data

• Competence, extirpation risk, and life history
• Modes of transmission
• Competition

1. Extending the framework

• Biodiversity and symbionts

Most processes non-specific to parasites

• how does host diversity affect symbiont diversity?

Similar to habitat area-heterogeneity trade-off in free living species

Role of parasitism vs. mutualism

San Francisco Bay Area amphibian parasites

• More data
• Many parasites are facultative
• Broader class of species interactions

1. Linking existing theory and data

• Competence, extirpation risk, and life history
• Modes of transmission
• Competition

1. Extending the framework

• Biodiversity and symbionts
• Scale transitions

Local dynamics

Local dynamics \(\rightarrow\) regional dynamics

Local dynamics \(\neq\) regional dynamics if

• local dynamics are non-linear
• densities vary spatially
• conditions vary spatially

(Chesson et al. 2005)

Most theory (but see Roche et al. 2012): short term

• instantaneous rates
• \(R_0\)
• force of infection

Most data: long-run

• prevalence
• seroprevalence
• density of infected hosts

1. Linking existing theory and data

• Competence, extirpation risk, and life history
• Modes of transmission
• Competition

1. Extending the framework

• Biodiversity and symbionts
• Scale transitions